Nirmal Malapaka from Wolfram Research, Inc.'s Technical Support told
me that at present, DSolve cannot handle boundary/initial conditions
in partial differential equations. Perhaps, some day (in the not too
distant future) Mathematica version ? will be able to solve these
types of problems. I know that software should never be expected to
substitute human creativity and ingenuity, but I love when "the
machine" can validate a result reached after the arduous ascension of
human analysis, determination, and sheer guts.
Thank you all for your help!